Journal article
Transport of interfaces with surface tension by 2D viscous flows
Interfaces and free boundaries, v 12(1), pp 23-44
01 Jan 2010
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We consider the problem of finding a global weak solution for two-dimensional, incompressible viscous flow on a torus, containing a surface-tension bearing curve transported by the flow. This is the simplest case of a class of two-phase flows considered by Plotnikov in [16] and Abels in [1]. Our work complements Abels' analysis by examining this special case in detail. We construct a family of approximations and show that the limit of these approximations satisfies, globally in time, an incomplete set of equations in the weak sense. In addition, we examine criteria for closure of the limit system, we find conditions which imply nontrivial dependence of the limiting solution on the surface tension parameter, and we obtain a new system of evolution equations which models our flow-interface problem, in a form that may be useful for further analysis and for numerical simulations.
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Details
- Title
- Transport of interfaces with surface tension by 2D viscous flows
- Creators
- David M. Ambrose - Drexel UniversityMilton C. Lopes Filho - Univ Estadual Campinas, UNICAMP, IMECC, Dept Matemat, BR-13083970 Campinas, SP, BrazilHelena J. Nussenzveig Lopes - Univ Estadual Campinas, UNICAMP, IMECC, Dept Matemat, BR-13083970 Campinas, SP, BrazilWalter A. Strauss - Brown University
- Publication Details
- Interfaces and free boundaries, v 12(1), pp 23-44
- Publisher
- European Mathematical Soc
- Number of pages
- 22
- Grant note
- 303.301/2007-4; 302.214/2004-6 / CNPq; Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) DMS-0926378; DMS-0405066 / NSF; National Science Foundation (NSF) 2007/51490-7 / FAPESP; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000275191500002
- Scopus ID
- 2-s2.0-77955065437
- Other Identifier
- 991019170503204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied